I have a Sony but have not had that problem with it. I took a look and they are more electronic than some so harder to test. Normally there is a little sensor that rides against the tape to check tape tension. when it reaches the end tape pulls tight and pushes a little bar down which stops the tape. For auto reverse there might also be something that senses something stopping a spindle. Not sure if this is any help. What model do you have? I could disect mine if it is the same.
Jim, March 2006